In 1960, Reed and Solomon suggest the codeword for a message $[x_0\ x_1\ \ldots\ x_k]$ as follows:
$$[P_{(0)}\ P_{(\alpha)}\ P_{(\alpha^2)}\ \cdots\ P_{(\alpha^{2^m-1})}]$$
Where
$$P_{(t)}=x_0 +x_1t+x_2t^2+\cdots +x_{k-1}t^{k-1}$$
And $\alpha$ is a generator of $GF(2^m)$. So the length of the codeword would be $2^m$.
However, today the RS code is usually considered a code of the length $2^m-1$. Why? And what is redundant?